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Proof step 7 from proof sgn-notsame (previous step)

sgn(boolvar ' + bits0) = boolvar0 ' + boolvar0 ', ∀ boolvar1. ¬ boolvar1 ∈ bits0 ∨ sgn(bits0) ≠ boolvar1 ' + boolvar1 ' ⊦ bits0.first ↔ boolvar, bits0 = [], ¬ boolvar0 ∈ bits0 ∧ ¬(boolvar0 ↔ boolvar)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits0, boolvar2, bits] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits0, boolvar2, bits